I would recommend the widest tires you can fit and if you are facing loads of flats a good puncture protectant tire will help! Continental Gatorskins from your local shop or an authorized online bike shop would be a good choice or the GatorHardshells but the ride is not as fun as it is a very stiff tire but decent puncture protection. A good Schwalbe tire in a similar format would be another choice but best to go to your local shop or at least an authorized online bike store. Also keep your tires properly inflated probably closer to the max on the tires.

However your flats are going to happen more shoving yourself all the way over. I don't know specific law in CT but if you can take your lane, take your lane don't give cars your lane so you can get flats. Always be confident and ride with that confidence and good spatial awareness. If you feel safer in the lane take the lane and just wave them past. It sucks sometimes but better you take the lane and they honk and yell "YERGABLURBAFURKADURKA" or whatever non-sense I cannot seem to hear then be shoved over into a dangerous shoulder or barely shoulder that causes damage to the bike and is not safe for you.

Also I would look at a more practical bike for your riding the Centurions have a cult following and aren't bad bikes but you will probably be limited in tire width and a wider tire at a lower pressure will be less susceptible to flats. Also with a more modern bike you could have the potential for tubeless and if you are riding more often going tubeless might help prevent flats or if not using something like Tannus inserts can help but they don't really work on skinny tires despite what Tannus says. Plus having two bikes allows you to do a lot more and also have a bike at the shop and one to ride so you don't have the down time.

Agreed with MikeWMass on carrying a spare tube, pump, tire levers and CO2 and knowing how to use all of that. It will help greatly.
"If it wasn't for bad luck I wouldn't have any luck at all" - various sources but the song Born Under a Bad Sign always makes me think of it.